(a) Suppose a = b = 1 in the Gompertz differential equation (7). Since the DE is aut...

(a) Suppose a = b = 1 in the Gompertz differential equation (7). Since the DE is autonomous, use the phase portrait concept of Section 2.1 to sketch representative solution curves corresponding to the cases .

(b) Suppose a = 1, b= -1 in (7). Use a new phase portrait to sketch representative solution curves corresponding to the cases

(c) Find an explicit solution of (7) subject to P(0) = P₀.